Calculus of Variations and Geometric Measure Theory

M. S. Gelli - D. Lučić

A note on BV and 1-Sobolev functions on the weighted Euclidean space

created by lučić on 07 Oct 2021
modified by gelli on 11 Apr 2023


Published Paper

Inserted: 7 oct 2021
Last Updated: 11 apr 2023

Year: 2021

ArXiv: 2110.02622 PDF


In the setting of the Euclidean space equipped with an arbitrary Radon measure, we prove the equivalence between several notions of function of bounded variation present in the literature. We also study the relation between various definitions of 1-Sobolev function.